Resistance

If you've had any experience with electronics, you may be wondering why you've never heard of this "conductance" before. You may be more familiar with the resistance $$R$$, the reciprocal of the conductance. $$R=\frc{G}$$ When resistance increases, conductance decreases, and the amount of current through the wire drops. The relationship between potential difference and current is given by $$\Dl V=IR$$ which is called Ohm's Law. The resistance of a wire is given by $$R=\rho \frac{L}{A}$$ where $$\rho=\frc{\sigma}$$ is the resistivity of the material of the wire: glass has a high resistivity and metal has a low resisitivity.

The SI units of resistance are ohms, written as Ω: $$[R]=\left[\frac{\Dl V}{I}\right]=\frac{V}{A}=\Omega$$ The units of conductance are inverse ohms, which goes by two different names: the official SI unit is the siemens (S), but I prefer calling it the mho ℧.

All objects and devices can be said to have a resistance, not just wires: but of course $$R=\rho L/A$$ doesn't work for a TV or a light bulb. In general, Ohm's Law actually defines the resistance of a device: hook up the device to a potential difference $$\Dl V$$, measure the current $$I$$ that flows through the device, and the resistance of the device is $$R=\frac{\Dl V}{I}$$
The resistance isn't necessarily constant: it is often a function of the potential difference. For example, a device called a diode only allows current to flow in one direction: it has a certain resistance in one direction, but if you hook it up to a battery backwards, the resistance becomes infinite. Devices where the resistance is independent of the potential difference are called ohmic devices. Wires are approximately ohmic *if too much current flows through a wire, it can heat up, which can change the resistivity of the material. Devices designed to have a specific resistance are often called resistors. In diagrams, resistors are traditionally represented by a zigzag, like this:

A typical carbon resistor
Interactive 10.4.1